论文标题
对随机混沌系统的路径灵敏度的重要性采样
Importance Sampling for Pathwise Sensitivity of Stochastic Chaotic Systems
论文作者
论文摘要
本文提出了一个新的Chaotic SDE的途径敏感性估计器。通过在原始SDE和扰动的SDE之间引入春季学期，我们通过重要性采样得出了一个新的估计器。与标准路径估计器的指数增加相比，新估计器的差异仅在时间$ t上线性增加。我们将估计器与Malliavin估计器进行比较，并将两个扩展到多级蒙特卡洛方法，从而进一步提高了计算效率。最后，我们还考虑将此估计量用于SDE，并具有较小的波动率，以近似混乱的odes不变度的敏感性。此外，Richardson-Romberg在波动率参数上的外推给出了更准确，更有效的估计器。数值实验支持我们的分析。
This paper proposes a new pathwise sensitivity estimator for chaotic SDEs. By introducing a spring term between the original and perturbated SDEs, we derive a new estimator by importance sampling. The variance of the new estimator increases only linearly in time $T,$ compared with the exponential increase of the standard pathwise estimator. We compare our estimator with the Malliavin estimator and extend both of them to the Multilevel Monte Carlo method, which further improves the computational efficiency. Finally, we also consider using this estimator for the SDE with small volatility to approximate the sensitivities of the invariant measure of chaotic ODEs. Furthermore, Richardson-Romberg extrapolation on the volatility parameter gives a more accurate and efficient estimator. Numerical experiments support our analysis.
